Yes, it only happened after the first start in the morning. I hope this isn't the problem with your car, though.

While the coolant temperature sensor theory sounds plausible, and is certainly worth checking, I can't imagine how it would stall the engine. If it were disconnected, a pre-determined default value would be used to allow the engine to run normally, more or less. The CEL would eventually light up as well.

Start your diagnosis with the simple stuff. On the car I worked on, I made sure the sensor connections were securely in place (air mass, CKP, etc), and checked for signs of corrosion. I left a fuel pressure gauge on the car overnight to make sure the fuel pressure came up quickly when the engine was first started. I had a volt-meter on the fuel pump to make sure I wasn't losing power. I used SDS to check the "Actual Values" being read in by the engine control module at the moment the engine was first cranked over.

I suspected the torque converter early on, but believe me, I didn't want to replace it only to find out later that the problem was a loose connector in the fuse box, or some other silly thing. I'm curious as to how this turns out. Keep us posted, and best of luck.